In this paper, we consider the measure determined by a fractional Ornstein-Uhlenbeck process. For such a measure, we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality. To this end, we also present the integration by parts formula for such a measure, which is obtained via its pull back formula and the Bismut method.

中文翻译：

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分数Ornstein-Uhlenbeck测度的表示和对数-Sobolev不等式

在本文中，我们考虑由分数Ornstein-Uhlenbeck过程确定的度量。对于这种度量，我们建立了representation表示定理的显式形式，并因此获得了对数-Sobolev不等式的显式形式。为此，我们还介绍了这种度量的分部公式，它是通过其拉回公式和Bismut方法获得的。